6] What is the Cartesian integral that represents the following polar integral 2r sin e cos 0 dr de ? a) s b) 7 ) S * xy dxdy xy dydx xy dydx 1- d) xy dxdy e) - Đi s xy dydx xy dydx g) None of them

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, Ie z2(2z – 37) | where C is the…

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Q: Use Green's Theorem to evaluate the line integral v+e*) dx + (6x+cosy) dy where C is the triangle…

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Q: Use Green's theorem to evaluate line integral (9y – In(x2 + y2)) dx + (2 arctan( (2)) dy, where C is…

A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

Q: 3.4.8 Evaluate the area of the surface z = 2-x² - y² lying above the (x, y) plane. (Hint: Use polar…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy – xy sinyz dz) is path independent and find its…

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Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - C: boundary of the region…

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Q: 6. Compute the area of the surface for 0 <u 1, 0 < v < using the first fundamental form..

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Q: 4. Change the Cartesian integral to an equivalent polar integral S'I SER dy dx e -(x²+y²) /2 re-r dr…

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Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

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Q: Consider the double integralf", * dydx. By converting to polar coordinates, the limits of…

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Q: 15- Evaluate the surface integral f, xy dswhere x is the part of the plaue y = 1-x-z that lies in…

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Q: Jse Green's theorem to evaluate the ne integral (2tan x _cos 2y³) dx + (7⁰s y + 2x (πº where is the…

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Q: 2. Use polar coordinate to evaluate the integral cVa2-x2 dydx (1+x²+y²)2

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0.…

A: To find point of intersection equate both r and find value of  θ which lie in the interval -π,π For…

Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: 6] What is the Cartesian integral that represents the following polar integral r'sin e cos e dr de?…

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Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Use the Cauchy integral formulas to evaluate the  ∮c eizcos z/ z2(2z -3π) dz,  where C is the region…

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Q: The double integral I = °S x2 + y? dydx in polar coordintes is:

A: Given integral is I=∫13∫1xx2+y2 dydx We have to change the given integral into the polar coordinate…

Q: Consider the double integralf, ,"* dydx. By converting to polar coordinates, the limits of…

A: Draw graph of upper limit of y which is equation of circle

Q: Consider the double integral dydx. By converting to polar coordinates, the limits of integration of…

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Q: Use the theorem on saddle-node bifurcations from the lecture' to show that i = sin(r) sin(r) +…

A: Given dxdt=sinrsinx+cosx-er. Let us prove that 0,0 is the saddle-node bifurcation.   Theorem:…

Q: 7. To convert the following cartesian integral to polar, the double integral becomes, * cos (x² +…

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Q: Consider the double integral dydx. By converting to polar coordinates, the limits of integration of…

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Q: 3. Evaluate the iterated integral Y arctan 2 dydx by converting to polar coordinates.

A: Polar coordinates for converting the iterated integral are: x = rcos(θ), y = rsin(θ)dydx = rdrdθ

Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: Use Green’s Theorem to evaluate the line integral   ∫_c  (x+ 2y^3)dx + (2x − 3y)dy   where C is the…

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Q: 2.1 Evaluate la Im(z – i)dz where C is the contour from z = 1+ 2i to z = i and from z = i to z = -i.…

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Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion

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Q: 12. Evaluate by using Stoke's Theorem [sin z de - cos x dy + sin y dz] where C is the boundary of…

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Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Although this integral could be written as 3 9-z2 (9 - x2 - z2) vx² + z²dz dx it's easier to convert…

A: Given  ∫-33∫-9-x29-x2(9-x2-z2)x2+z2dzdx

Q: Use Green's Theorem to evaluate the line integral Lv+e) dx + (3x+cosy) dy where C is the triangle…

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Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: 21. (y² dx + x² dy)

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Q: Calculate the area bounded by the circler = 2 and the rays 0 = 1t and e = n as an integral in polar…

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: evaluate the contour integral z^2 -z^4/z-1)cos(z)where c:|z|=4

A: Introduction: Cauchy's integral formula is very significant in complex analysis. It helps to…

Q: Calculate the line integral f(-102 + 4z + 5) de + (-7z – Oy? – by – 4) dy, where Dis the annulus…

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Q: to find the aren ruse 2) Use a polar integral enclosed by the three-petaled r = singe

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Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Let C be the unit circle {z : |z| = 1} with positive orientation. By any method, compute the…

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Q: Evaluate the integral ∫(1,2,3)(5,9,−4)y dx+x dy+2 dz by finding parametric equations for the line…

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Q: Consider the polar curve r= 2 sin(0) + 3 ,0ses27, whose plot is shown below. 2.0 1.5 1.0 0.5…

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Q: Find the curl of U = pz² cos p a, +z sin? o az. z2 2z sin o cos Ap sin ф аz а, + 2z cos ф аф + p2 2z…

A: This question is related to coordinate system and curl of a vector function and vector calculus, We…

Q: Express R C Im(4iz + ¯z) dz where C is the directed line segment that joins the point −3 + 4i to the…

A: Consider the given integral which is required to solve.

Q: Consider the double integralf dydx. By converting to polar coordinates, the limits of integration of…

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Q: 5. Use polar coordinates to combine the sum NZ p* xy dydx + S 4-x2 L*y dydx + L,* xy dydx + La** xy…

A: Given: ∫121∫1-x2xxy dydx +∫12∫0xxy dy dx+∫22∫04-x2xy dy dx

Q: 2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z…

A: Formula: By Stoke's theorem we have ∮C F · dr¯  =∫t=t1t=t2 F¯(r(t))r'(t) dt, where r(t) is…

Q: Use Green's Theorem to evaluate the line integral along the gi | 4y3 dx - 4x³ dy Cis the circle x2 +…

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